Allotropes standard state

The reference temperature is usually 298.15 K (25°C). Where there is more than one allotrope, then the stable form of the solid is chosen. In spite of the definition of the standard state, it is occasionally convenient to speak of the standard state of the gas at 25°C for a substance which is actually liquid or solid at this temperature and a pressure of 1 atm water is a compound for which this is often done. 

Four allotropes of phosphorus are known, the hexagonal /(-white, stable only below —77°C, the cubic a-white trap 44.1°C), the violet, and the black (which is thermodynamically the most stable). The a-white form is usually taken as the standard state. The violet is obtained by continued heating at 500°C of a solution of phosphorus in lead. When a-white phosphorus is heated to 250 C in the absence of air, a red variety (rap 590CC) is obtained which is believed to consist of a mixture of the a-white and violet allotropes, although the studies of the violet component in the mixture have shown that at least four polymorphic forms of red (violet) phosphorus exist. 

Several comments need to be made concerning the state of aggregation of the substances. For gases, the standard state is the ideal gas at a pressure of 1 bar this definition is consistent with the standard state developed in Chapter 7. When a substance may exist in two allotropic solid states, one state must be chosen as the standard state for example, graphite is usually chosen as the standard form of carbon, rather than diamond. If the chemical reaction takes place in a solution, there is no added complication when the standard state of the components of the solution can be taken as the pure components, because the change of enthalpy on the formation of a compound in its standard state is identical whether we are concerned with the pure... 

The molar volume is usually given for a solid substance at 298.15 K (temperature of standard state). Apart from temperature and density, it depends on phase and allotrope of the substance. 

The most stable allotrope is orthorhombic sulfur (the a-form and standard state of the element) and it occurs naturally as large yellow crystals in volcanic areas. At 367.2 K, the ot-form transforms reversibly into monoclinic sulfur (j3-form). Both the a- and jB-forms contain Sg rings the density of the a-form is 2.07gcm , compared with... 

The carbon atom has four valence electrons and four valency orbitals. To that extent it is electron precise, and can form four bonds per atom. It does this in its various allotropes, graphite being its standard state. The structure of graphite is shown in Figure 6.4 and consists of hexag-onally bonded sheets of carbon atoms that are 335 pm apart. The... 

The sea level reference point for all enthalpy expressions is called the standard enthalpy of formation (MIf). Substances ate said to be in the standard state at 1 atm, hence the term standard enthalpy. The superscript represents standard-state conditions (1 atm), and the subscript f stands for formation. By convention, the standard enthalpy of formation of any element in its most stable form is zero. Take the element oxygen as an example. Molecular oxygen (O2) is more stable than the other allotropic form of oxygen, ozone (O3), at 1 atm and 25°C. Thus, we can write = 0, but... 

The formation reaction of a substance is the reaction in which the substance, at a given temperature and in a given physical state, is formed from the constituent elements in their reference states at the same temperature. The reference state of an element is usually chosen to be the standard state of the element in the allotropic form and physical state that is stable at the given temperature and the standard pressure. For instance, at 298.15 K and 1 bar the stable allotrope of carbon is crystalline graphite rather than diamond. 

Hess s law of heat summation (6.7) standard state (6.8) allotrope (6.8) reference form (6.8) standard enthalpy of formation (standard heat of formation) (6.8)... 

The standard state of an element is the pure substance at 1 bar (previously, 1 atm) and having the specified allotropic form, if necessary. Although there is no specified standard temperature, many references use 25.0°C as the designated temperature. 

Notes. In the case of a single oxide (or hydroxide) existing in different allotropic states, indicated by the letters a, b, c, d, etc. the oxides are arranged in descending order of stability, i.e. in ascending order of standard chemical potentials (expressed for an identical chemical formula). 

With the exception of a few allotropic elements, the necessary input parameters to Eqs (6.1) or (6.2) are not available to establish the lattice stabilities of metastable structures. Therefore an alternative solution has to be found in order to achieve the desired goal. This has evolved into a standard format where the reference or ground state Gibbs energy is expressed in the form of genera] polynomials which reproduce assessed experimental Cp data as closely as possible. An example of such a standard formula is given below (Dinsdale 1991) ... 

By way of illustrations we display in Fig. 1.17.2a plot of the molar heat capacity of oxygen under standard conditions. The plot of Cp vs. In T is then used to determine the entropy of oxygen from the area under the curves. Note that the element in the solid state exists in three distinct allotropic modifications, with transition temperatures close to 23.6 and 43.8 K the melting point occurs at 54.4 K, and the boiling point is at 90.1 K. All the enthalpies of transition at the various phase transformations are accurately known. An extrapolation procedure was employed below 14 K, which in 1929 was about the lower limit that could conveniently be reached in calorimetric measurements. 

The reference form of an element for the purpose of specifying the formation reaction is usually the stablest form (physical state and allotrope) of the element under standard thermodynamic conditions. The reference form of oxygen at 25°C is 02(g) the reference form of carbon at 25°C is graphite. ... 

At 25 °C, the standard entropy of any substance is the energy dispersed into one mole of that substance at 25 °C, which depends on the number of places to put energy within the substance. The factors that affect the number of places to put energy— and therefore the standard entropy—include the state of the substance, the molar mass of the substance, the particular allotrope, its molecular complexity, and its extent of dissolution. Let s examine each of these separately. 

Relative Standard Entropies Allotropes As mentioned previously, some elements can exist in two or more forms—called allotropes— in the same state of matter. For example, the allotropes of carbon include diamond and graphite— both solid forms of carbon. Since the arrangement of atoms within these forms is different, their standard molar entropies are different ... 

---